Presbyopia correction program

ABSTRACT

A method of generating a computer program for control of an apparatus for photorefractive treatment of presbyopia by ablation of corneal tissue or a contact lens, comprising the following steps:
     (a) electing an eye model,   (b) measuring the pupil diameter of the patient at far distance mesopically and at short distance photopically,   (c) selecting wanted short and far distances regarding optimum sight,   (d) calculating a global optimum regarding curvature (1/R) and asphericity (Q) of the cornea on the basis of the results obtained in steps (a) (b) and (c) by means of optical ray tracing and minimal spot diameter at the retina, and   (e) deriving the computer program in accordance with the results of step (d).
 
Alternatively step (d) includes determining a central steep island with a diameter in the range of 2 to 4 millimeters at the cornea and calculating a curvature and asphericity in the rest of the cornea.

CROSS REFERENCE

This application was originally filed as Patent Cooperation TreatyApplication No. PCT/EP2006/007895 filed Aug. 9, 2006, which claimspriority of European Application No. 05018062.9, filed Aug. 19, 2005.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a United States national phase application ofco-pending international patent application number PCT/EP2006/007895,filed Aug. 9, 2006, the disclosure of which is incorporated herein byreference.

BACKGROUND

The present invention is concerned with a method of generating acomputer program for control of an apparatus capable to ablate cornealtissue or a contact lens for treatment of presbyopia.

Presbyopia is the lack of capability of the eye lens to accommodate forfar distance and near distance.

The prior art knows many optical approaches to presbyopia includingreading glasses, monovision, multifocal contact lenses, intraocularimplants, and accommodative intraocular lenses. None of these attemptscan restore accommodation but all represent compromises to establish amore or less fair near vision at the costs of far vision. Some methodswere designed to restore accommodation by means of scleral expansionnear the ciliary body, however, have so far failed to prove efficacy.

In refractive laser surgery, first “presbyopia corrections” have beenreported in the early nineties (Moreira H, Garbus J J, Fasano A, ClaphamL M, Mc Donnell P J; Multifocal Corneal Topographic Changes with ExcimerLaser photorefractive Keratectomy; Arch Ophthalmol 1992; 100: 994-999;Anschütz T, Laser Correction for Hyperopia and Presbyopia, IntOphthalmol Clin 1994; 34: 105-135). However, such techniques have notgained wide clinical acceptance. More sophisticated presbyopiacorrection profiles have been proposed including an induced centralsteep island (CSI), U.S. Pat. No. 5,533,997 (Ruiz) and WO93/25166 (King,Klopotek). The present invention partially refers to the concept of CSIdisclosed in the afore-mentioned patents. Also decentered steep areashave been proposed, see U.S. Pat. No. 5,314,422 to Nizzola, andBauerberg J , Centered vs. Inferior off-center Ablation to CorrectHyperopia and Presbyopia, J Refract Surg 1999. The prior art alsosuggests a near vision zone in the mid-periphery of the cornea, seeTelandro A, Pseudo-accommodative Cornea: a new Concept for Correction ofPresbyopia, J Refract Surg 2004; 20 :S714- S717; and Cantu R, Rosales MA, Tepichin E, Curioca A, Montes V, Bonilla J; Advanced Surface Ablationfor Presbyopia using the Niek EC-5000 Laser, J Refract Surg 2004, 20:S711-S713.

SUMMARY

The present invention aims at an effective method for presbyopiacorrection and provides a method of generating a computer program forcontrol of a laser system for photorefractive treatment of presbyopia byablation of tissue from or in the cornea or from a contact lens.

To this end, the method of generating a computer program for control ofan apparatus for photorefractive surgery comprises the following steps:

-   (a) selecting an eye model,-   (b) measuring the pupil diameter of the patient at far distance    mesopically and at short distance photopically,-   (c) selecting wanted short and far distances regarding optimum    sight,-   (d) calculating a global optimum regarding curvature (1/R) and    asphericity (Q) of the cornea on the basis of the results obtained    in steps (a) (b) and (c) by means of optical ray tracing and minimal    spot diameter at the retina and-   (e) deriving the computer program in accordance with the results of    step (d).

This method of determining global optimum for curvature and asphericitycreates a purely aspheric shape including a small amount of myopia withincreased depths of focus. A stronger refractive power is obtained fornear in the central area surrounded by a mid-periphery with less power.The aspheric global optimum includes an even naturally occurring cornealasphericity that provides a variable pseudoaccommodation depending onthe asphericity constant Q and the pupil diameter change amplitudeduring the near reflex.

According to an alternative embodiment of the invention a computerprogram for control of an apparatus for photorefractive surgery isgenerated by the following steps:

-   (a) selecting an eye model,-   (b) measuring the pupil diameter of the patient at far distance    mesopically and at short distance photopically,-   (c) selecting wanted short and far distances regarding optimum    sight,-   (d) determining a central steep island with diameter in the range of    2 to 4 millimeter and a refractive height of 1 to 4 diopters at the    cornea and calculating a curvature and asphericity in the rest of    the cornea depending on the central island selected, and-   (e) deriving the computer program in accordance with the results of    step (d).

This technique results in a multifocal cornea with two main foci. Againa stronger refractive power is obtained for near in the central areasurrounded by a mid-periphery of less power. The two main driving forcesfor this multifocal CSI are, on the one hand, the pupil size thatdecreases during focusing near objects (pupillary near reflex) and, onthe other hand, also the depths of focus is increased.

This CSI-configuration is a corneal analogon to the artificial bifocal,intraocular lens (IOL). Due to its increased depths of focus, theadvantage of the CSI-technology is a twice better retinal image of nearobjects as compared to the globally optimized shape and a four timesbetter image compared to the non-accommodated emmetropic eye.

According to a preferred embodiment of the present invention, theoptimal configuration (computer program) is tested for patientsatisfaction prior to surgery using contact lenses. When applying one ofthe two afore-mentioned ablation techniques, first contact lenses can beformed in accordance with the generated computer program and the soformed lenses are tested by the patient for a few days. Therefore thepresent invention also provides a method of generating a computerprogram product for control of an apparatus capable of ablating contactlenses.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a pair of charts mapping spot diameter in the retina for farand near objects in the context of an emmetropic eye (no accommodation).

FIG. 2 is a pair of charts mapping spot diameter in the retina for farand near objects in the context of a global optimum.

FIG. 3 is a pair of charts mapping spot diameter in the retina for farand near objects in the context of a central steep island.

FIG. 4 is a graph mapping spot diameter in the retina between a centralsteep island and an off-center steep island.

DETAILED DESCRIPTION

In the following the invention is described in more detail with regardto specific embodiment.

1. Theoretical Eye Model

The eye model used here is based on the model of Liou and Brennan (LiouH L, Brennan N A, Anatomically accurate, finite Model Eye for opticalModeling; J Opt Soc Am A Opt Image Sci Vis 1997; 14: 1684-1695). Thismodel is characterized by aspheric anterior and posterior corneal andlenticular surfaces. In addition, it includes a linear refractive indexgradient of Δn=0.2 inside the lens. The parameters for the emmmetropiceye are listed in Table 1. The anterior cornea was approximated by abiconoid surfacez=(x2/Rx+y2/Ry)/(1+(1−(1+Qx)x2/Rx2−(1+Qy)y2/Ry2)1/2)  1.where 1 /Rx,y are the curvatures and Qx,y are the asphericity constantsin the corresponding main meridians, the positive z-direction pointsinto the eye, the positive y-direction upwards. The reference wavelengthis 555 nm. In order to include the Stiles-Crawford effect a transmissionfilter is introduced (Moon P, Spencer D E, On the Stiles-CrawfordEffect, J Opt Soc Am 1944; 34: 319-32)T(r)=exp(−ar2)  2.with the apodization constant a=0.105 and r the radial distance from thecenter of the pupil.

To model central or decentered steep islands, cubic spline functions areintroduced with steps of 0.5 mm radial distance from the apex of thecornea. All optical surfaces are centered on the optical axis. A pupildiameter of 5 mm is used for simulation of the far distant (objectdistance 5 m) and 2.5 mm for near (object distance 0.4 m) visionconfiguration. The object is a point light source located 1° up.Additional (reading) glasses have a distance of 12 mm from the vertex ofthe cornea.

The quality of the retinal image is described either by the “rms spotdiameter” or the “rms wavefront error” similar to the techniquepublished earlier (Seiler, T Reckmann W, Maloney R K, Effectivespherical Aberration of the Cornea as a quantitative Descriptor of theCornea, J Cataract Refract Surg. 1993; 19 Suppl: 155-65).

All calculations can be performed with a commercially available opticaldesign program such as, e.g., the optical design program ZEMAX EE,version March 2004 (Zemax Development Cooperation, San Diego, Calif.).Useful is an optimization process aiming on a minimal spot diameter inthe retina (circle of least confusion), but depending on the problemalso modulation transfer function, wavefront error and point spreadfunction can be used as optimization operands.

The quality of the retinal image is determined in near and far distantconfiguration for the following scenaria (Table 2): (1) the emmetropiceye optimized regarding asphericity and eye length, (2) the globaloptimum for simultaneous near and far distant vision optimized regardingR and Q, (3) central steep island with a diameter of 3 mm and arefractive height of 3D optimized regarding R and Q, (4) scenario (3)but the central steep island is decentered towards inferior in 0.5mm-steps up to 3 mm.

2. Results

Optimization of eye length and asphericity in the emmetropic eye for fardistance vision yielded approximately physiologic values (Table 1): aneye length of 24.01 mm and a corneal asphericity constant of −0.158. Theminimal spot diameter in the retina d=1.396 microns as well as thewavefront error of 0.034 waves are close to the diffraction limit.Introducing a corneal astigmatism of 0.75 D increases the minimal spotdiameter to 29.662 microns and the wavefront error to 1.338 waves, avalue that is clinically observed.

Comparing the spot diameter in the retina for the far and near distantobject reveals in the emmetropic eye (no accommodation) a shift of thefocus of 890 microns behind the retina (FIG. 1) which can be shiftedback into the retina by a reading glass of 2.32 diopters with a vertexdistance of 12 mm.

FIG. 2 demonstrates the spot diameter through the retina for the globaloptimum regarding R and Q (GO) in the far and near object configuration.It is worth mentioning that the two configurations differ not only bythe distance of the object but also by the pupil diameter. The spotdiameter in the retina increases to 37.61 microns for the far distantobject and decreases to 34.22 microns for the near object (Table 2).Comparing the optimized emmetropic eye (scenario 1) with the globaloptimum (scenario 2) the difference in a case of a CSI with 3 mm indiameter and 3 diopters in height consists in an increase in centralcorneal power of 1.4 diopters (myopia) and a more prolate corneal shapeQGO=−0.68. Again, by using a reading glass of 1.01 diopters the focuscan be shifted into the retina yielding a spot diameter of 3.56 microns.The other CSI configurations yield different values for curvature 1/Rand asphericity constant Q.

The spot diameter through the retina for the central steep island withoptimized R and Q for simultaneous far and near vision is depicted inFIG. 3. Whereas for the far distant object the spot diameter iscomparable to that in the global optimum (GO) it is better by a factorof approximately 2 for near vision. However, reading glasses cannotimprove this result any more.

Decentration of the steep island degradates the quality of the retinalimage which is shown in FIG. 4. Compared to the central steep island adecentration of for example lmm results in a 1.6-fold worsening for farand 4.7-fold worsening for near vision. Again, reading glasses can onlymarginally improve near vision.

3. Discussion

The major finding of this study is that there are configurations of thecorneal shape that represent a clinically meaningful compromise of minorlosses in far distance vision with improvement of near vision. The twomost attractive approaches are (1) the central steep island combinedwith appropriate curvature and asphericity in the rest of the cornea and(2) the global optimum for curvature and asphericity. Whereas the firstproposal means a multifocal cornea with two main foci, the second one isa purely aspheric shape creating a small amount of myopia with increaseddepth of focus. Both corneal shapes provide a stonger refractive powerfor near in the central area surrounded by a mid-periphery with lesspower. The two main driving forces of the multifocal CSI- as well as theaspheric GO-shape are, on one hand, the pupil size that decreases duringfocusing near objects (pupillary near reflex) and, on the other hand,also the depth of focus is increased in both optical scenaria.

The CSI-configuration is a corneal analogon to the artificial bifocalIOL (Jacobi K W, Nowak M R, Strobel J, Special Intraocular Lenses,Fortschr Ophthalmol 1990; 87: S29-S32) with all its known advantages anddisadvantages such as loss in contrast sensitivity, halos, glare, andreduced visual satisfaction (Leyland M D, Langan L, Goolfee F, Lee N,Bloom P A, Prospective Randomized Double-Masked Trial of BilateralMultifocal, Bifocal or Monofocal Intraocular Lenses, Eye 2002; 16:481-490); (Pieh S, Lackner B, Hanselmayer G, Zohrer R, et al., Halo Sizeunder Distance and Near Conditions in Refractive Multifocal IntraocularLenses, Br J Ophthalmol. 2001; 85: 816-821); (Lesueur L, Gajan B, NardinM, Chapotot E, Arne J L, Comparison of visual Results and Quality ofVision between Two Multifocal Intraocular Lenses. Multifocal Siliconeand Bifocal PMMA, J Fr Ophthalmol. 2000; 23: 355-359);(Knorz M C,Seiberth V, Ruf M, Lorger C V, Liesenhoff H, Contrast Sensitivity withmonofocal and biofocal Intraocular Lenses, Ophthalmologica 1996; 210:155-159); (Haaskjold E, Allen E D, Burton R L, et al., ContrastSensivity after Implantation of Diffractive Bifocal and MonofocalIntraocular Lenses, J Cataract Refract Surg 1998; 24: 653-658).

In contrast, the aspheric GO includes an even naturally occuring cornealasphericity that provides a variable pseudoaccomodation depending on theasphericity constant Q and the pupil diameter change amplitude duringthe near reflex.

Due to its increased depth of focus the advantage of the CSI is a twicebetter retinal image of near objects compared to the GO-shape and fourtimes better compared to the non-accommodated emmetropic eye, but alsodue to the increased depth of focus one of its disadvantages is theinability to improve both near and far vision by means of spectacles. Inaddition, the effect of the CSI is critically dependent on centration:already at a decentration of 0.1 mm the advantage of the CSI comparedwith GO is gone and a degradation of the retinal image for distancevision by a factor of 1.3 happens. Using modem eye-trackers centrationis achieved reliably, however, there is a principal problem because theCSI should be centered regarding the visual axis and the crossing pointof the visual axis through the cornea is uncertain and hard todetermine. Reasonable centration is much easier obtained using theGO-approach because it does not contain such a localized opticalinhomogeneity.

A major disadvantage of a multifocal optics of the eye is the loss inmesopic vision as measured in low contrast visual acuity and contrastsensitivity that has been repeatedly reported after multifocalintraocular implants satisfaction (Leyland M D, Langan L, Goolfee F, LeeN, Bloom P A, Prospective randomized double-masked Trial of BilateralMultifocal, Bifocal or Monofocal Intraocular Lenses, Eye 2002; 16:481-490); (Lesueur L, Gajan B, Nardin M, Chapotot E, Arne J L,Comparison of visual Results and Quality of Vision between TwoMultifocal Intraocular Lenses. Multifocal Silicone and Bifocal PMMA, JFr Ophthalmol. 2000; 23: 355-359);(Knorz M C, Seiberth V, Ruf M, LorgerC V, Liesenhoff H, Contrast Sensitivity with monofocal and biofocalIntraocular Lenses, Ophthalmologica 1996; 210: 155-159); (Haaskjold E,Allen E D, Burton R L, et al., Contrast Sensivity after Implantation ofDiffractive bifocal and monofocal Intraocular Lenses, J Cataract RefractSurg 1998; 24: 653-658).

Many patients complain about an increase of halos (Pieh S, Lackner B,Hanselmayer G, Zohrer R, et al., Halo Size under distance and nearConditions in Refractive Multifocal Intraocular Lenses, Br J Ophthalmol.2001; 85: 816-821). Regarding these optical side effects we would liketo cite a recent statement of Georges Baikoff (Baikoff G, Matach G,Fontaine A, Ferraz C, Spera C, Correction of Presbyopia with refractivemultifocal Phakic Intraocular Lenses, J Cataract Refract Surg. 2004; 30:1454-1460): “Optical defects are inevitable with multifocal IOLs; . . .”. Although this argument holds mainly for the clearly multifocalCSI-shape of the cornea a similar loss in contrast sensitivity isexpected to occur also with strongly aspheric corneas. However, anasphericity constant Q of −0.7 as intended in the global optimum (GO) isonly −0.5 away from the average (Kiely P M, Smith G, Carney L G, TheMean Shape of the human Cornea, Optica Acta 1982; 29: 1027-1040) andcompares favorably with the up to three times larger changes in theasphericity constant after standard myopic LASIK of up to +1.5 (HolladayJ T, Dudeja D R, Chang J. Functional Vision and corneal Changes afterLaser in Situ Keratomileusis determined by Contrast Sensitivity, GlareTesting, and Corneal Topography. J Cataract Refract Surg. 1999; 25:663-669); (Koller T, Iseli H P, Hafezi F, Mrochen M, Seiler T, Q-Factorcustomized Ablation Profile for the Correction of Myopic Astigmatism, JCataract Refract Surg. (2005 submitted). Also, emmetropic or hyperopiceyes receiving a hyperopia correction for attempted slight myopia formonovision experience a shift in asphericity towards prolate that is inthe order of −0.5 (Chen C C, Izadshenas A, Rana M A, Azar D T, CornealAsphericity after hyperotic Laser in Situ Keratomileusis. J CataractRefract Surg, 2002; 28: 1539-1545).

The currently most frequently used concept of presbyopia correction isthe monovision approach where the dominant eye is corrected foremmetropia and the non-dominant for minor myopia ranging from −0.5 D to−2.0 D (Miranda D, Krueger R R, Monovision Laser in Situ Keratomileusisfor pre-presbyopic and prescbiopic Patients, J Refract Surg. 2004; 20.:325-328); (Mc Donnell P J, Lee P, Spritzer K, Lindblad A S, Hays R D,Assiocations of Presbyopia with vision-targeted health-related Qualityof Life, Arch Ophthalmol. 2003; 121: 1577-1581); (Johannsdottir K R,Stelmach L B, Monovision: A Review of the scientific Literature, OptomVis Sci. 2001; 78: 646-651); Greenbaum S, Monovision Pseudophakia, JCataract Refract Surg. 2002; 28: 1439-1443); (Jain S, Ou R, Azar D T,Monovision Outcomes in presbyopic Individuals after refractive Surgery,Ophtalmology. 2001; 108: 1430-1433). In clinical surgery practice theoptimal configuration is tested for patient satisfaction prior tosurgery using contact lenses. A similar strategy may be appropriate whenapplying one of the two presented ablation profiles including binocularversus monocular multifocal/aspheric treatment. Assuming that in thefuture we will have access to such a set of contacts and the patient maydecide for surgery after a few days of simulation of his future opticswe are still at risk of dissatisfaction. In a study testing monovisionin presbyopic patients by means of contact lenses the immediate responsewas not a good predictor for satisfaction after two weeks (Du Toit R,Ferreira J T, Nel Z J, Visual and nonvisual Variables implicated inMonovision Wear, Optom Vis Sci. 1998; 75: 119-125).

To facilitate understanding the correlation of minimal spot diameter andvisual acuity the spot diameters in the retina for various degrees oflow myopia are considered. With a myopia of −0.5 diopters an uncorrectedvision of approximately 20/30 may be obtained under scotopic lightningconditions which corresponds to a spot diameter in the retina of 40microns. This may serve as a gross reference for the two configurationsCSI and GO. With CSI a near visual acuity of 20/25 and a far distant VAof 20/30 seems to be obtainable, good lightning conditions andappropriate pupil diameters provided. With the GO approach both near andfar VA are at approximately 20/30 with the option to improve near VA to20/20 with reading glasses, an option that we do not have in CSI-treatedeyes. It is clear that only prospective controlled studies will give usbetter information about the visual acuities achieved after presbyopiacorrections.

The last and most critical point that needs to be discussed is that anypresbyopia “correction” necessarily is a kind of compromise. Whateverone wins in the near domain must be lost in far distance vision and viceversa. Having this in mind and considering the dependence of the opticalresult on pupil sizes under various conditions and its centration it isobvious that any ablative presbyopic correction should be handled as acustomized treatment and simulated preoperatively by means of contactlenses. One of the strongest predictors of a satisfying outcome ofrefractive surgery is the patient's expectation. Especially withpresbyopia correction the balance of the optically possible and theindividually desirable has to be made preoperatively. Also important inthis context is the reversibility of the operation: simple monovisionand GO is easy to correct by means of a reoperation, whereas the CSIprofile is more difficult to reverse although recently progress has beenreported using advanced customized ablation by means of Zernike andFourier algorithms (Hafezi F, Iseli H P, Mrochen M, Wullner C, Seiler T,A New Ablation Algorithm for the Treatment of Central Steep Islandsafter Refractive Laser Surgery, J Cataract Refract Surg. (2005submitted).

4. The Method

Resulting from the above findings, the present invention proposes thefollowing method:

The shape of the cornea, represented by its curvature (1/R), theasphericity (Q) and a central steep island (CSI) are formed individually(i.e. for a particular patient) such that the optical quality(sharpness) of the image at the retina is optimal simultaneously at thefollowing two configurations: (a) far object (e.g. the distance to theeye is 5 m or more), the pupil diameter is large (e.g. 5 mm, generallyspeaking larger than 3, 5 or 4 mm) and (b) near object (e.g. the objectis 0, 4 m from the eye, generally speaking nearer than 0, 6 m), thepupil diameter is small (e.g. smaller than 3 mm).

Such an individually adapted configuration can be simulated by contactlenses used by the patient. This includes the option of monovision, e.g.the dominant eye for far sight and the non-dominant eye for presbyopiacorrection.

The method can be summarized as follows:

(1) Measuring the pupil diameter for a far distance mesopically and ashort distance photopically,

(2) Defining the distances with intended optimum sight for far distanceand near distance,

(3) Calculating the global optimum for R and Q by means of opticaldesigner software (for example ZEMAX) on the basis of a selected eyemodel (e.g. Liou-Brannen), using, optionally, the refinement disclosedin (Seiler T, Reckmann W, Maloney R K, Effective spherical Aberration ofthe Cornea as a quantitative Descriptor of the Cornea, J CataractRefract Surg. 1993; 19 Suppl: 155-65). This may or may not include aCSI,

(4) Manufacturing a corresponding contact lens (if not available onstock) that is stabilised on the eye regarding the optical axis,

(5) If the patient is satisfied with the result the cornea can betreated accordingly.

The CSI typically has a diameter of 3 mm at the cornea (the range is 2to 4 millimetre) and a refractive power of 3 dpt (a range of 2 to 4dpt). The parameters are entered into the above-stated software by meansof cubic spline functions, for example.

For an average eye (R=7.77 mm Q=-0.15) a myopia, without CSI, of −1.5dpt and Q-factor of −0.7 is obtained. Including CSI a small hyperopia of+0.9 dpt and a Q-value of +0.22 should be aimed at.

When determining the global optimum the wanted configurations for nearand far are defined (distances, pupil diameters) and the starting valuesof R and Q (where required including astigmatism) are entered into theprogram. Thereafter, two runs for optimization are started (oneincluding CSI, the other without CSI). The values of R and Q are enteredas operands which are freely variable and the program is iteratively rununtil the quality of the picture at the retina, defined by the minimumspot radius at the retina or the MTF (Modulation Transfer Function) orthe point spread function is optimized. The such optimized opticalconfiguration of the cornea is aimed at when ablating the cornea or thelens respectively.

TABLE 1 Parameters of the optimized emmetropic eye model curvatureradius asphericity apex position refractive Surface R (mm) Q (mm) indexant. cornea 7.77 −0.158 0.00 1.376 post. cornea 6.4 −0.6 0.52 1.336pupil 13.0 0 3.68 1.336 ant. lens 12.4 −0.94 3.68 1.453 * post. lens−8.1 −0.96 7.70 1.336 retina 12.0 0 24.01 — *The lens includes a lineargradient of refractive index increasing from 1,453 at the surfaces to1,652 in the center

TABLE 2 Quality of the retinal image (point light source, λ = 550 nm)minimal spot diameter (microns) far distance near distance opticalscenario (5 m) (0.4 m) 1. emmetropic eye optimized (Q = −0.158) 1.4065.48 2. corneal astigmatism 0.75D (Q = −0.158). 29.66 76.85 3. globaloptimum for R and Q 37.61 34.22 (R = 7.55 ; Q = −0.68) 4. central steepisland optimized R and Q 44.47 17.62 (R = 7.92; Q = +0.22) 5. decenteredsteep island, decentered by 68.84 82.85 1mm, optimized R and Q (R = 7.68; Q = −0.42) 6. centered steep annulus optimized R and Q 130.1 77.62 (R= 7.21; Q = −1.72)

1. A method of generating a computer program for control of an apparatusfor photorefractive treatment of presbyopia by ablation of cornealtissue or a contact lens, the method comprising the steps of (a)selecting an eye model, (b) measuring the pupil diameter of the patientat far distance mesopically and at short distance photopically, (c)selecting wanted short and far distances regarding optimum sight, (d)calculating a global optimum regarding curvature (1/R) and asphericity(Q) of the cornea on the basis of the results obtained in steps (a) (b)and (c) by means of optical ray tracing and minimal spot diameter at theretina, and (e) deriving the computer program in accordance with theresults of step (d).
 2. A method of generating a computer program forcontrol of an apparatus for photorefractive treatment of presbyopia byablation of corneal tissue or a contact lens, the method comprising thesteps of (a) selecting an eye model, (b) measuring the pupil diameter ofthe patient at far distance mesopically and at short distancephotopically, (c) selecting wanted short and far distances regardingoptimum sight (d) determining a central steep island with a diameter inthe range of 2 to 4 millimeters at the cornea and calculating acurvature and asphericity in the rest of the cornea and (e) deriving thecomputer program in accordance with the results of step (d).
 3. A methodaccording to one of the claims 1 or 2 wherein said eye model is theLiou-Brennan model.
 4. A method according to claim 1, wherein in step(d) the global optimum is calculated such that the optical quality(sharpness) of the image at the retina is optimized for simultaneousoptimum at the following conditions: 1.) far object and pupil diameterlarger than 3, 5 millimeter and 2.) near object and pupil diameter of 2,5 mm or less.
 5. A method according to claim 2, wherein in step (d) thedetermination is such that the optical quality (sharpness) of the imageat the retina is optimized for simultaneous optimum at the followingconditions:) 1.) far object and pupil diameter larger than 3, 5millimeter and 2.) near object and pupil diameter of 2, 5 mm or less. 6.A method according to claim 2, wherein in step (d) the central steepisland has a refractive power of 2 to 4 diopters.